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2013 | OriginalPaper | Buchkapitel

8. Implementing the Example: One Time Period

verfasst von : Prof. PierCarlo Nicola

Erschienen in: Efficiency and Equity in Welfare Economics

Verlag: Springer Berlin Heidelberg

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Abstract

To not overburden the calculations that follow, in this chapter, the examples implemented will consider only what happens in a single time period. Nonetheless, it is possible to extend the calculations and the results to a sequence of time periods, as will be done in Chap. 9.

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Vorheriges Kapitel A Summary Example

Nächstes Kapitel Dynamics: Many Time Periods

The entire population is split in deciles, when considering individual incomes.

While we assume that the law holds for all values of individual incomes, Pareto found that his law applies only to individual incomes greater than a given value.

In statistical terms, each of the ten ranges in which the data is grouped is also called decile.

The functions selected do not contain a productivity parameter, because the total productivity parameter, a, is directly applied to the social production function, Φ, summarizing the parameters of the individual production functions. This choice considers two important characteristics of Φ: on one hand social production is the result of an interaction among the contributions of individual agents; on the other hand the choice of a must be calibrated in order to obtain an economically reasonable potential rate of growth for the economy being considered.

Another way of choosing a is to select the value of the total productivity parameter which agrees with the initial data previously chosen, namely the value that, under the given initial individual incomes, generates a social production value equal to the selected initial value, i.e. \(\bar{Y } = 1794000\). The value thus is a = 998. 6221562, and it is obtained by calculating 1794000/1351998*752.5837.

Let’s remember that, in the previous chapter we chose to consider γ, the overall returns to scale parameter, as not greater than 1. In this chapter we always have γ = 1.

Here we consider that the total productivity parameter is determined by the principle on which it is calculated.

Remembering that overall initial income amounts to 1,794,000, an even distribution among economic agents would severely impoverish the entire economy!

This is equivalent to imposing a uniform 20% income tax on those agents who are not very poor!

From here on, θ = 1, with no loss of generality.

Of course, as a byproduct of this calculation, we obtain the transfer vector, \(v = ({v}_{1},{v}_{2},\ldots,{v}_{1000})\), verifying \({x}_{j} = {y}_{j} + {v}_{j}\) for every j.

A smaller choice of q, for instance q = 0. 1, of course has a weaker effect on final income distribution.

Note: as a byproduct of this calculation, we obtain the vector of transfers \(v = ({v}_{1},{v}_{2},\ldots,{v}_{1000})\), verifying \({x}_{j} = {y}_{j} + {v}_{j}\) for every j.

Here too, a smaller value of q, for instance q = 0. 1, has a weaker effect on final income redistribution.

Once more, note that, as a byproduct of this calculation, we obtain the vector of income transfers, \(v = ({v}_{1},{v}_{2},\ldots,{v}_{1000})\), verifying \({x}_{j} = {y}_{j} + {v}_{j}\) for every j.

Here too, smaller choices of q, for instance q = 0. 1, have a weaker effect on final income redistribution.

Titel: Implementing the Example: One Time Period
verfasst von: Prof. PierCarlo Nicola
Verlag: Springer Berlin Heidelberg
Buch: Efficiency and Equity in Welfare Economics
Print ISBN: 978-3-642-30070-7

Electronic ISBN: 978-3-642-30071-4

Copyright-Jahr: 2013
DOI: https://doi.org/10.1007/978-3-642-30071-4_8

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